Solve for $x$ and $y$ using elimination. ${x-6y = -53}$ ${-x+5y = 44}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-y = -9$ $\dfrac{-y}{{-1}} = \dfrac{-9}{{-1}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {x-6y = -53}\thinspace$ to find $x$ ${x - 6}{(9)}{= -53}$ $x-54 = -53$ $x-54{+54} = -53{+54}$ ${x = 1}$ You can also plug ${y = 9}$ into $\thinspace {-x+5y = 44}\thinspace$ and get the same answer for $x$ : ${-x + 5}{(9)}{= 44}$ ${x = 1}$